Systems of Cosserat--Zhilin in Newtonian Mechanics

Abstract

Mechanical systems of Cosserat--Zhilin are introduced as the main object of Newtonian (non--relativistic) mechanics on the base of new notions of vector calculus - sliders and screw measures (bi-measures). The differential equations of motion are derived for different types of Cosserat--Zhilin systems in the case where Stocks theorem is applicable. The paper defines multiplicative groups which represent the measure of stress as a (well-defined) linear isotropic map of {strain} tensor or tensor of {strain velocities} for classical and polar continua in 2- and 3-dimensional cases.